# Measurement of the inelastic pp cross section at √s = 7 TeV with the CMS detector

## Abstract

A new method to measure the inelastic pp cross section has been developed based on the assumption that pile-up events are randomly distributed according to a Poisson probability. This method relies only on the accurate knowledge of the CMS tracking system and it does not depend upon a specific Monte Carlo simulation. The value of the cross section for events with at least 2 charged particles with $|\eta|<2.4$ and $p_\perp > 200$ MeV is determined to be $\sigma_{2-trks} = 58.7 \pm 2.0 \; (Syst) \pm 2.4 \; (Lum) \; {\rm mb}$. Using model-dependent extrapolations, the value for the total inelastic $pp$ cross section is determined to be $\sigma_{inel}(pp) = 68.0 \pm 2.0 \; (Syst) \pm 2.4 \; (Lum) \; \pm 4 (Ext.) \; {\rm mb}$.

## Approved Plots from FWD-11-001 PAS ( click on plot to get .pdf )

Figure Abbreviated Caption
Fraction of generated events with a given vertex track multiplicity accepted by the selection criteria $NDOF \ge 0.5$ and with either 2 (empty circles) or 3 (solid circles) reconstructed tracks. The plot shows this fraction evaluated with 2 different versions of PYTHIA.
Comparison data - reweighted Monte Carlo. Each plot shows, as function of luminosity, the number of events with a given value of vertices, from 1 to 11. The first 9 plots contain the data used in this analysis.
Data and Monte Carlo distribution in each of the 13 luminosity bins, from 0.05~to~0.7~$\cdot 10^{30}\; {\rm cm^{-2} \; s^{-1}}$.
Fraction of events with n pile-up events as a function of luminosity. The dotted line is a Poisson fit.
$\chi^2$/NDOF (top) and $\sigma(pp)$ values (bottom) for each of the fit of Figure~\ref{fig:final}. The dashed line is the result of the fit to the 9 $\sigma(pp)$ values. The fits are for events with at least 2 charged particles.

 Comparison between the CMS results and several Monte Carlo models for events with at least 2, 3 and 4 charged particles in $abs(\eta)<2.4$ and $p_t >$ 200 MeV. Systematic uncertainties shown by the inner red error bars and luminosity uncertainty by the outer black bars. Monte Carlo predictions have a common uncertainty of $~1$ mb

 Compilation of total inelastic $pp$ and $p\bar{p}$ cross section values. CMS analysis uncertainty is shown in dark blue while the model-dependent extrapolation is shown in light blue.

 Generator level $\xi$ distribution of several MC models (PYTHIA, PHOJET, SIBYLL, QGSJET, EPOS) for all events and for events with at least 2 charged particles, each with $p_t > 200$ MeV in the range $abs(\eta)< 2.4$.

## Additional approved plots for FWD-11-001 PAS ( click on plot to get .pdf )

Figure Description
Number of vertices as a function of the bunch instantaneous luminosity.
Number of vertices during the 2010 run period
The x-axis of the plot is the distance between two vertices while on the y axis it shows their combined track multiplicity. This plot shows that vertices that are closer to each other more than ∼ 0.6mm are merged together.
Uncorrected pile-up distribution. The dashed lines are a fit using a Poisson distribu- tion, see eq.1.
Monte Carlo events fitted with a Poisson function for each value of pile-up events
χ2 (top) and σ values (bottom) for each of the fit of Figure 17. The dashed line is the result of the fit to the 9 σ values. The generator value of σinel = 56.2 mb is well reproduced by the measurement.

 Fraction of secondary vertices with and without the requirement on the transverse position of the vertex to be within ±0.06 mm from the beam line.
-- NicoloCartiglia - 01-Aug-2011

Topic attachments
I Attachment History Action Size Date Who Comment
gif Blind2.gif r1 manage 29.1 K 2011-08-01 - 22:26 NicoloCartiglia
gif Data_MC_Lumibins.gif r1 manage 30.2 K 2011-08-01 - 13:22 NicoloCartiglia
gif FInal_plots_05.gif r1 manage 21.1 K 2011-08-01 - 13:28 NicoloCartiglia
gif MC_64_564.gif r1 manage 17.1 K 2011-08-01 - 22:33 NicoloCartiglia
gif MC_Sigma_chi2.gif r1 manage 10.0 K 2011-08-01 - 22:34 NicoloCartiglia
gif MC_data_64_05.gif r1 manage 26.1 K 2011-08-01 - 13:22 NicoloCartiglia
gif Secondary.gif r1 manage 8.3 K 2011-08-01 - 23:08 NicoloCartiglia
gif Sigma_chi_final_65_05_2trk.gif r1 manage 9.5 K 2011-08-01 - 13:29 NicoloCartiglia
gif Tot_inel.gif r1 manage 146.0 K 2011-08-01 - 13:48 NicoloCartiglia
gif Uncor_plots_05.gif r1 manage 16.1 K 2011-08-01 - 22:28 NicoloCartiglia
gif Vtx_Eff_2_3_trk.gif r1 manage 14.2 K 2011-08-01 - 13:09 NicoloCartiglia Fig1_gif
gif Vtx_vs_lumi.gif r1 manage 12.3 K 2011-08-01 - 22:24 NicoloCartiglia
gif csi.gif r1 manage 11.0 K 2011-08-01 - 14:14 NicoloCartiglia
gif nvertexes.gif r1 manage 11.0 K 2011-08-01 - 22:26 NicoloCartiglia
gif sigma_com_part.gif r1 manage 10.3 K 2011-08-01 - 13:34 NicoloCartiglia
gif xi_models.gif r2 r1 manage 16.6 K 2011-08-01 - 14:01 NicoloCartiglia
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Topic revision: r2 - 2011-08-01 - NicoloCartiglia

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